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# If P^2 + Q^2 =1, is P – Q =1?

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If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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25 Aug 2012, 05:32
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If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1
(2) P is a positive integer.
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Joined: 02 Sep 2009
Posts: 58464
Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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25 Aug 2012, 05:41
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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Updated on: 25 Aug 2012, 05:57
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.
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Originally posted by EvaJager on 25 Aug 2012, 05:52.
Last edited by EvaJager on 25 Aug 2012, 05:57, edited 1 time in total.
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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25 Aug 2012, 05:56
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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25 Aug 2012, 06:01
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.

No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from $$P^2+Q^2=1$$).
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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25 Aug 2012, 06:04
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.

Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 --> Q=0.

EvaJager wrote:
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.

If the first statement were P-Q=1, then it would be sufficient, since that's exactly what we are asked - to find whether P-Q=1.
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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25 Aug 2012, 06:15
Bunuel wrote:
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.

Do you mean for (2)? Here, since we determined that P=1 we can solve P^2+Q^2=1 to get the value of Q: 1^2+Q^2=1 --> Q=0.

EvaJager wrote:
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Should be P - Q, but this doesn't really change anything in the answer.
After you correct your post, you can erase mine.

If the first statement were P-Q=1, then it would be sufficient, since that's exactly what we are asked - to find whether P-Q=1.

OMG...I'm an astronaut today...
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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21 Oct 2013, 11:46
EvaJager wrote:
shivanigs wrote:
Thanks Bunuel! Silly question but i will still ask.How can we be sure that Q is also an integer? We have not been given any info on Q.

No need for Q to be an integer. Since P = 1, it comes out that Q = 0 (from $$P^2+Q^2=1$$).

hi,
not sure, if iota (i) concept can be applied in here ..

i thought, in verifying S2,
P=2, Q^2=-3, Q=sqrt3 * iota
so, in this case also, p^2+Q^2=1
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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06 Feb 2016, 13:17
Hi Bunuel

Can you please tell me why A cant be sufficient using below approach?

Given P^2 + Q^2 = 1.

P-Q = 1 => SQUARING BOTH SIDES => P^2 + Q^2 -2PQ = 1
=> 1 -2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So our question becomes whether one of p or q is zero?

Now looking at A :

P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So this should be sufficient right?

Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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07 Feb 2016, 04:34
neeraj609 wrote:
Hi Bunuel

Can you please tell me why A cant be sufficient using below approach?

Given P^2 + Q^2 = 1.

P-Q = 1 => SQUARING BOTH SIDES => P^2 + Q^2 -2PQ = 1
=> 1 -2PQ = 1 (SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So our question becomes whether one of p or q is zero?

Now looking at A :

P+Q = 1 => Squaring both sides => P^2 + Q^2 + 2PQ = 1 => 1+2PQ = 1 ( SUBSTITUTING THE VALUE OF P^2 + Q^2)
=> PQ = 0
So this should be sufficient right?

Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

You cannot square. If p - q = -1, then (p - q)^2 would be equal to 1^2 but p - q = -1 is not equal to 1.
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Re: If P^2 + Q^2 =1, is P – Q =1?  [#permalink]

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16 Mar 2019, 04:39
Bunuel wrote:
If P^2 + Q^2 =1, is P – Q =1?

(1) P + Q = 1 --> if P=1 and Q=0, then the answer is YES but if P=0 and Q=1, then the answer is NO. Not sufficient.

(2) P is a positive integer --> since P is a positive integer, then from P^2+Q^2=1 we'll have that P can only be 1 (if P is an integer more than 1, then P^2+Q^2>1). Now, if P=1 then Q=0 (again from P^2+Q^2=1), hence the answer whether P-Q=1 is YES. Sufficient.

Hi, Any reason why we shouldn't rephrase the question ?

P-Q=1? => squaring both the sides => p^2+q^2-2pq=1 => since P^2 +Q^2 =1 => 2pq=0 => pq =0 ?????
Re: If P^2 + Q^2 =1, is P – Q =1?   [#permalink] 16 Mar 2019, 04:39
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